Composite Figures

1
9-3
Composite Figures
Warm Up
Lesson Presentation
Lesson Quiz
Holt Geometry
2
Warm Up Find the area of each figure. 1. a
rectangle in which b 14 cm and h 5 cm 2. a
triangle in which b 6 in. and h 18 in. 3. a
trapezoid in which b1 7 ft, b2 11 ft, and h
3 ft
A 70 cm2
A 54 in2
A 27 ft2
3
Objectives
Use the Area Addition Postulate to find the areas
of composite figures. Use composite figures to
estimate the areas of irregular shapes.
4
Vocabulary
composite figure
5
A composite figure is made up of simple shapes,
such as triangles, rectangles, trapezoids, and
circles. To find the area of a composite figure,
find the areas of the simple shapes and then use
the Area Addition Postulate.
6
Example 1A Finding the Areas of Composite
Figures by Adding
Find the shaded area. Round to the nearest tenth,
if necessary.
Divide the figure into parts.
area of half circle
7
Example 1A Continued
area of triangle
area of the rectangle
A bh 20(14) 280 mm2
shaded area
50? 280 84 521.1 mm2
8
Example 1B Finding the Areas of Composite
Figures by Adding
Find the shaded area. Round to the nearest tenth,
if necessary.
Divide the figure into parts.
area of parallelogram
A bh 8(5) 40ft2
area of triangle
shaded area
40 25 65 ft2
9
Check It Out! Example 1
Find the shaded area. Round to the nearest tenth,
if necessary.
Area of rectangle
A bh 37.5(22.5)
843.75 m2
Area of triangle
Total shaded area is about 1781.3 m2.
937.5 m2
10
Example 2 Finding the Areas of Composite Figures
by Subtracting
Find the shaded area. Round to the nearest tenth,
if necessary.
area of a triangle
area of the half circle
Subtract the area of the half circle from the
area of the triangle.
area of figure
234 10.125? 202.2 ft2
11
Example 2 Finding the Areas of Composite Figures
by Subtracting
Find the shaded area. Round to the nearest tenth,
if necessary.
area of circle
A ?r2 ?(10)2 100? cm2
area of trapezoid
area of figure
100? 128 ? 186.2 cm2
12
Check It Out! Example 2
Find the shaded area. Round to the nearest tenth,
if necessary.
area of circle
A ?r2 ?(3)2 ? 28.3 in2
area of square
A bh ? (4.24)(4.24) ? 18 in2
area of figure 28.3 18 10.3 in2
13
Example 3 Fabric Application
A company receives an order for 65 pieces of
fabric in the given shape. Each piece is to be
dyed red. To dye 6 in2 of fabric, 2 oz of dye is
needed. How much dye is needed for the entire
order?
To find the area of the shape in square inches,
divide the shape into parts.
The two half circles have the same area as one
circle.
14
Example 3 Continued
The area of the circle is ?(1.5)2 2.25? in2.
The area of the square is (3)2 9 in2.
The total area of the shape is 2.25? 9 16.1
in2.
The total area of the 65 pieces is 65(16.1)
1044.5 in2.
15
Check It Out! Example 3
The lawn that Katie is replacing requires 79
gallons of water per square foot per year. How
much water will Katie save by planting the
xeriscape garden?
Area times gallons of water
375.75(79) 29,684.25
Subtract water used
29,684.25 6,387.75
23,296.5 gallons saved.
16
To estimate the area of an irregular shape, you
can sometimes use a composite figure. First,
draw a composite figure that resembles the
irregular shape.
Then divide the composite figure into simple
shapes.
17
Example 4 Estimating Areas of Irregular Shapes
Use a composite figure to estimate the shaded
area. The grid has squares with a side length of
1 ft.
Draw a composite figure that approximates the
irregular shape. Find the area of each part of
the composite figure.
18
Example 4 Continued
area of triangle a
area of triangle b
area of rectangle c
A bh (2)(1) 2 ft2
area of trapezoid d
Area of composite figure
1 0.5 2 1.5 5 ft2
The shaded area is about 5 ft2.
19
Check It Out! Example 4
Use a composite figure to estimate the shaded
area. The grid has squares with side lengths of 1
ft.
Draw a composite figure that approximates the
irregular shape. Find the area of each part of
the composite figure.
20
Check It Out! Example 4 Continued
area of triangle
area of half circle
area of rectangle
A lw (3)(2) 6 ft2
The shaded area is about 12 ft2.
21
Lesson Quiz Part I
Find the shaded area. Round to the nearest tenth,
if necessary.
1.
38.6 cm2
2.
50 ft2
22
Lesson Quiz Part II
3.
Mike is remodeling his kitchen. The countertop he
wants costs 2.70 per square foot. How much will
Mike have to spend on his remodeling project?
64.80
23
Lesson Quiz Part III
4.
Use a composite figure to estimate the shaded
area. The grid has squares with side lengths of 1
cm.
about 8.5 cm2